Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.     

Global distribution, structure, and solar wind control of low altitude current sheets at Mars

We present the results of the first systematic survey of current sheets encountered by Mars Global Surveyor in its ∼400 km mapping orbit. We utilize an automated procedure to identify over 10,000 current sheet crossings during the ∼8 year mapping mission. The majority of these lie on the nightside and in the polar regions, but we also observe over 1800 current sheets at solar zenith angle <60°. The distribution and orientation of current sheets and their dependence on solar wind drivers suggests that most magnetotail current sheets have a local induced magnetospheric origin caused by magnetic field draping. On the other hand, most current sheets observed on the day side likely result from solar wind discontinuities advected through the martian system. However, the clustering of low altitude dayside current sheet crossings around the perimeters of strongly magnetized crustal regions, and the smaller than expected rotations in the IMF draping direction, suggest that crustal magnetic fields may also play an indirect role in their formation. The apparent thicknesses of martian current sheets, and the characteristics of electrons observed in and around the current sheets, suggest one of two possibilities. Martian current sheets at low altitudes are either stationary, with thicknesses of a few hundred km and currents carried by low energy (<10 eV) electrons, or they move at tens of km/s, with thicknesses of a few thousand km and currents carried by ions.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

On sheared magnetic field structures containing neutral points

This paper discusses the occurence of current sheets near the separatrix in sheared magnetic field structures containing an x-type neutral point, as suggested by a number of previous authors. Our approach is based on selfconsistent theory. In analogy to the theory of quasistatic convection by Grad, we interpret the break-down of the quasistatic theory near the separatrix as evidence for the occurence of a boundary layer. In particular, this picture suggests large (however integrable) current sheets, with the current flowing parallel to the poloidal magnetic field. This concept is also tested by numerical computations. Here the discretization procedure simulates those physical effects that in a real case would keep the current from becoming infinitely large. The results fully confirm the formation of current sheets. Our findings have potential applications to energy storage for solar flares and to the heating of the solar corona.     

Association of solar prominences and coronal magnetic sheets from their observed correlation with type III radiobursts

It is shown that coronal structures in which are excited type III bursts (observed with the Nançay radioheliograph) have a good correlation with existence of plage filaments.By accepting that type III bursts reveal the presence of coronal magnetic neutral sheets, an interpretation of results is proposed and discussed in relation with theories of formation of filaments from coronal neutral sheets. It is suggested that the delay of one day observed in several cases between the type III burst occurrence and the filament appearance may be of the order of the filament condensation time from the neutral sheet.     

Particle distributions and X-ray spectra in single or multiple solar current sheets

The acceleration of charged particles in a site of magnetic reconnection is analysed by detailed numerical simulations. Single or multiple encounters of the particles with Harris-type reconnecting current sheets (RCSs) are modelled as an overall stochastic process taking place within an active region. RCS physical parameters are selected in a parameter space relevant to solar flares. Initially, the charged particles form a thermal (Maxwellian) distribution corresponding to coronal temperature  ≃2 × 10⁶ K  . Our main goal is to investigate how the acceleration process changes the shape of the particles' kinetic energy distribution. The evolution of the kinetic energy distribution, calculated numerically after one encounter of the particles with a single RCS, is found to be in good agreement with our previously published analytical formulae. In the case of consecutive encounters, we find that the kinetic distribution tends to converge to a practically invariant form after a relatively small number of encounters. We construct a discrete stochastic process that reproduces the numerical distributions and we provide a theoretical interpretation of the asymptotic convergence of the energy distribution. We finally compute the theoretical X-ray spectra that would be emitted by the simulated particles in a thick target model of radiation.     

EIDOSCOPE: particle acceleration at plasma boundaries

We describe the mission concept of how ESA can make a major contribution to the Japanese Canadian multi-spacecraft mission SCOPE by adding one cost-effective spacecraft EIDO (Electron and Ion Dynamics Observatory), which has a comprehensive and optimized plasma payload to address the physics of particle acceleration. The combined mission EIDOSCOPE will distinguish amongst and quantify the governing processes of particle acceleration at several important plasma boundaries and their associated boundary layers: collisionless shocks, plasma jet fronts, thin current sheets and turbulent boundary layers. Particle acceleration and associated cross-scale coupling is one of the key outstanding topics to be addressed in the Plasma Universe. The very important science questions that only the combined EIDOSCOPE mission will be able to tackle are: 1) Quantitatively, what are the processes and efficiencies with which both electrons and ions are selectively injected and subsequently accelerated by collisionless shocks? 2) How does small-scale electron and ion acceleration at jet fronts due to kinetic processes couple simultaneously to large scale acceleration due to fluid (MHD) mechanisms? 3) How does multi-scale coupling govern acceleration mechanisms at electron, ion and fluid scales in thin current sheets? 4) How do particle acceleration processes inside turbulent boundary layers depend on turbulence properties at ion/electron scales? EIDO particle instruments are capable of resolving full 3D particle distribution functions in both thermal and suprathermal regimes and at high enough temporal resolution to resolve the relevant scales even in very dynamic plasma processes. The EIDO spin axis is designed to be sun-pointing, allowing EIDO to carry out the most sensitive electric field measurements ever accomplished in the outer magnetosphere. Combined with a nearby SCOPE Far Daughter satellite, EIDO will form a second pair (in addition to SCOPE Mother-Near Daughter) of closely separated satellites that provides the unique capability to measure the 3D electric field with high accuracy and sensitivity. All EIDO instrumentation are state-of-the-art technology with heritage from many recent missions. The EIDOSCOPE orbit will be close to equatorial with apogee 25-30 RE and perigee 8-10 RE. In the course of one year the orbit will cross all the major plasma boundaries in the outer magnetosphere; bow shock, magnetopause and magnetotail current sheets, jet fronts and turbulent boundary layers. EIDO offers excellent cost/benefits for ESA, as for only a fraction of an M-class mission cost ESA can become an integral part of a major multi-agency L-class level mission that addresses outstanding science questions for the benefit of the European science community.     

Preflare conditions,changes and events

Prefiare conditions, changes and events are loosely categorized as distinct, evolutionary or statistical. Distinct preflare phenomena are those for which direct physical associations with flares are implied. Also, they are not known to occur in a like manner during the absence of flares. These include the early stage of filament eruptions within active centers, preflare vortical structures, some transient X-ray emitting features, 5303 Å accelerating coronal arches, and increases in circular polarization at cm wavelengths. Evolutionary preflare changes are considered to be any long-term effect that may be related to the flare build-up even though the same changes may occur in the absence of flares. This category covers the development of current sheets or strongly sheared magnetic fields, evolving magnetic features, emerging flux regions, the development of satellite fields around sunspots, the evolution of reverse polarity field configurations, the merging of adjacent active centers, sunspot motions and the development of velocity patterns. Statistical preflare changes logically include both distinct and evolutionary preflare changes. However, in addition, there are preflare conditions and events that are not necessarily linked to the flare in either a direct physical or indirect evolutionary way. Such parameters or events that may only be statistically significant are certain magnetic field properties, the brightness of active centers at various wavelengths, the previous occurrence of flares and subflares, increased turbulence in filaments and certain radio events.     

Filamentary structures in planetary nebulae

We have studied small-scale, filamentary features in 14 planetary nebulae and found that some structures are recurrent and shaped like the letters V and Y, with the apex or stem pointing toward the central parts of the nebula. Two such filaments containing dust, one in NGC 3132 and one in NGC 7293, were investigated in more detail. The mass and density of the filaments were obtained from extinction measurements, and their physical properties were derived. We propose that the structures are confined by magnetic fields, and derive magnetic field strengths of about 10⁻⁸ T, in line with earlier estimates. We also estimate the magnitude of the electric currents that we expect are generated in these dynamic systems. We propose a theory where the magnetic fields control the sculpting and evolution of small-scale filaments. This theory demonstrates how the substructures may form magnetized flux ropes that are twisted around each other, in the shape of double helices. Similar structures, and with similar origin, are found in many other astrophysical environments.     

Discrete subresolution structures in the solar transition zone

During operations on the Spacelab-2 Shuttle mission, the NRL High Resolution Telescope and Spectrograph (HRTS) recorded spectra of a variety of solar features in the 1200–1700 Å wavelength region which contains spectral lines and continua well suited for investigating the temperature minimum, the chromosphere and transition zone. These data show that, at the highest spatial resolution, the transition zone spectra are broken up from a continuous intensity distribution along the slit into discrete emission elements. The average dimensions of these discrete transition zone structures is 2400 km along the slit, but an analysis of their emission measures and densities shows that the dimensions of the actual emitting volume is conciderably less. If these structures are modelled as an ensemble of subresolution filaments, we find that these filaments have typical radii of from 3 to 30 km and that the cross-sectional fill factor is in the range from 10^–5 to 10^–2. The transport of mass and energy through these transition zone structures is reduced by this same factor of 10^–5 to 10^–2 which has significant consequences for our understanding of the dynamics of the solar atmosphere. Because the HRTS transition zone line profiles are not broadened by resolved large-spatial-scale solar velocity fields, the line widths of the Civ lines have been analyzed. The average line width is 0.195 Å (FWHM) and requires an average nonthermal velocity of 16 km s^–1 (most-probable) or 19 km s^–1 (root-mean-square) which is lower than previously observed values.     

A new model for the distribution of flare energies

A new model is presented for the distribution of solar (and stellar) flare energies. Flares are assumed to result from energy release in multiple reconnecting current sheets (RCSs) in the solar corona. The model takes into account both the dynamical evolution of separate RCSs and their interaction by virtue of coalescence. Thus an attempt is made to generalize previously suggested avalanche and RCS models for the flare frequency distribution. The number of RCSs is not specified and the strength of their interaction is governed by a coalescence parameter. Under quite general assumptions, the resulting distribution can be approximated by a power law with the slope 3/2 < < 7/4, as required by numerous observations. A softer distribution of numerous nanoflares, responsible for the coronal heating, is also possible under suitable choice of parameters.     

Derivation of density and temperature from the Cassini–Huygens CAPS electron spectrometer

In this paper we present two methods to derive electron fluid parameters from the CAPS–ELS spectrometer on board the Cassini spacecraft currently in orbit around Saturn. In the first part of the paper we give a basic overview of the instrument and describe the challenges inherent in the derivation of density and temperature values using these techniques. We then describe a method to calculate electron moments by integrating the particle distribution function. We also describe a second technique in which we fit the electron energy spectrum with a Gaussian curve and use the peak energy of this curve to derive density and temperature values. We then compare the two methods with particular emphasis on their application to Cassini SOI observations in the saturnian environment and point out the limitations of the two techniques. We will show that results from the two very different methods are in agreement when the physical properties of the environment and of the observed electron populations have been inferred from inspection of the raw data. Finally we will suggest future developments that will remove these limitations.     

Prolate Jaffe models for galaxies

We introduce a class of prolate Jaffe models for elliptical galaxies, which are a further extension of Jaffe's spherical models of axisymmetric elliptical systems, and study the properties of their densities, circular velocities, velocity dispersions and two-integral even distribution functions. The form of the potential allows the density to be expressed simply as a function of the potential and radial coordinate R . The models have finite total mass and their densities at large distances decay radially as r ⁻⁴, except on the major axis, where the densities decay as r ⁻³. It is known from Hunter's formulae that the velocity dispersions for prolate models can be expressed in terms of elementary functions of R and z , unlike those for the oblate Jaffe models recently given by Jiang, and that the prolate models have anisotropic velocity distributions. Thus the prolate models are easier to study than the oblate models. It is also found that the two-integral even distribution functions on the physical boundary of the galaxies increase monotonically with the relative energy, for the prolate models. Furthermore, numerical calculation shows that the two-integral even distribution functions generated from their densities are non-negative, even for very 'squeezed' prolate Jaffe models. However, the edge-on projected surface densities for these prolate models cannot be expressed as simply as for the oblate models.     

Nonlinear Evolution of Kinetic Alfvén Waves and Filament Formation

The transfer of wave energy to plasma energy is a very crucial issue in coronal holes and helmet streamer regions. Mixed mode Alfvén waves, also known as kinetic Alfvén wave (KAW) can play an important role in the energization of the plasma particles because of their potential ability to heat and accelerate the plasma particles via Landau damping. This paper presents an investigation of the growth of a Gaussian perturbation on a non-uniform kinetic Alfvén wave having Gaussian wave front. The effect of the nonlinear coupling between the main KAW and the perturbation has been studied. The dynamical equations for the field of the main KAW and the perturbation have been established and their semi-analytical solution has been obtained in the low (β≪ m_e/m_i≪ 1) and the high (β≫ m_e/m_i≪ 1) β cases. The critical field of the main KAW and the perturbation has been evaluated. Nonlinear evolution of the main KAW and the perturbation into the filamentary structures and its dependence on various parameters of the solar wind and the solar corona have been investigated in detail. These filamentary structures can act as a source for the particle acceleration by wave particle interaction because the KAWs are mixed modes and Landau damping is possible. Especially, in the solar corona, the low β and the high β cases could correspond to the coronal holes and the helmet streamer. The presence of the primary and the secondary filaments of the perturbation may change the spectrum of the Alfvénic turbulence in the solar wind.     

Localized magnetic reconnection as a cause of extraplanar diffuse ionized gas in the Galactic halo

Many observations indicate the occurrence of ionized gas in the distant haloes of galaxies (including our own). Since photoionization by stars (mainly O stars, young stars or evolved low-mass stars depending on the kind of galaxy) does not seem to be exclusively responsible for the ionization of the hydrogen filaments that should otherwise cool fast and recombine quickly, the question arises which extra energy source can produce the quasi-stationary ionization. We show that stationary localized magnetic reconnection in current filaments may contribute to the ionization of the extraplanar halo gas. In these filaments magnetic energy is dissipated. Consequently, the ionized as well as the neutral component is heated and re-ionized on a time-scale significantly shorter than the recombination time-scale. The amount of energy required for efficient re-ionization can in principle easily be provided by the free magnetic energy. We present quasi-static models that are characterized by plasma temperatures and densities that agree well with the observed values for the diffuse ionized gas component of the interstellar medium. Plasma–neutral gas fluid simulations are made to show that the recombination-induced dynamical reconnection process indeed works in a self-regulatory way.     

On neutral sheets in the solar wind

The structure and dynamics of neutral sheets in the solar wind is examined. The internal magnetic topology of the sheet is argued to be that of thin magnetic tongues greatly distended outward by the expansion inside the sheet. Due to finite conductivity effects, outward flow takes place across field lines but is retarded relative to the ambient solar wind by the reverse J×B force. The sheet thickness as well as the internal transverse magnetic field are found to be proportional to the electrical conductivity to the inverse one third power. Estimating a conductivity appropriate for a current carried largely by the ions perpendicular to the magnetic field, we find sheet dimensions of the order of 500km representative for the inner solar corona. For a radial field of strength 1/2G at 2R , the transverse field there is about 2 × 10^–3G and decreases outward rapidly.The energy release in the form of Joulean dissipation inside the sheet is estimated. It is concluded that ohmic heating in current sheets is not a significant source of energy for the overall solar wind expansion, mainly because these structures occupy only a small percentage of the total coronal volume. However, the local energy release through this mechanism is found to be large - in fact, over 7 times that expected to be supplied by thermal conduction. Therefore, ohmic heating is probably a dominant energy source for the dynamical conditions within the sheet itself.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Monte-Carlo simulation of Mercury's exosphere

Because of its proximity to the Sun and its small size, Mercury has not been able to retain its atmosphere and only a thin exosphere surrounds the planet. The exospheric pressure at the planetary surface is approximately 10⁻¹⁰ mbar, set by the Mariner 10 occultation experiment. The existence of gaseous species H, He, and O has been established by Mariner 10. In addition Na, K, and Ca have been observed by ground based instrumentation. Other elements are expected to be found in Mercury's exosphere since the total pressure of the known species is almost two orders of magnitude less than the exospheric pressure.It is intended to measure these exospheric particle densities in situ with an instrument on board of ESA's BepiColombo Mercury Planetary Orbiter (MPO) spacecraft. Since the expected exospheric densities are very small we developed a Monte-Carlo computer model to investigate if such a measurement is feasible along the MPO spacecraft orbit. We model energy and ejection angle distributions of the particles at the surface, with the emission process determining the actual distribution functions. Our model follows the trajectory of each particle by numerical integration until the particle hits Mercury's surface again or escapes from the calculation domain. Using a large set of these trajectories bulk parameters of the exospheric gas are derived, e.g., particle densities for various atomic and molecular species. Our study suggests that a mass spectrometric measurement is feasible and, at least at MPO's periherm, all species that are released from the surface will be observed.     

Some interesting topics provoked by the solar filament research in the past decade

Solar filaments are an intriguing phenomenon, like cool clouds suspended in the hot corona.Similar structures exist in the intergalactic medium as well. Despite being a long-studied topic, solar filaments have continually attracted intensive attention because of their link to coronal heating, coronal seismology, solar flares and coronal mass ejections(CMEs). In this review paper, by combing through the solar filament-related work done in the past decade, we discuss several controversial topics, such as the fine structures, dynamics, magnetic configurations and helicity of filaments. With high-resolution and highsensitivity observations, combined with numerical simulations, it is expected that resolving these disputes will definitely lead to a huge leap in understanding the physics related to solar filaments, and even shed light on galactic filaments.     

Developing an Advanced Automated Method for Solar Filament Recognition and Its Scientific Application to a Solar Cycle of MLSO Hα Data

We developed a method to automatically detect and trace solar filaments in Hα full-disk images. The program is able not only to recognize filaments and determine their properties, such as the position, the area, the spine, and other relevant parameters, but also to trace the daily evolution of the filaments. The program consists of three steps: First, preprocessing is applied to correct the original images; second, the Canny edge-detection method is used to detect filaments; third, filament properties are recognized through morphological operators. To test the algorithm, we successfully applied it to observations from the Mauna Loa Solar Observatory (MLSO). We analyzed Hα images obtained by the MLSO from 1998 to 2009 and obtained a butterfly diagram of filaments. This shows that the latitudinal migration of solar filaments has three trends in Solar Cycle 23: The drift velocity was fast from 1998 to the solar maximum, after which it became relatively slow. After 2006, the migration became divergent, signifying the solar minimum. About 60 % of the filaments with latitudes higher than 50^° migrate toward the polar regions with relatively high velocities, and the latitudinal migrating speeds in the northern and the southern hemispheres do not differ significantly in Solar Cycle 23.     

Numerical simulations of kinetic Alfvén waves to study spectral index in solar wind turbulence and particle heating

We present numerical simulations of the modified nonlinear Schrödinger equation satisfied by kinetic Alfvén waves (KAWs) leading to the formation of magnetic filaments at different times. The relevance of these filamentary structures to solar wind turbulence and particle heating has also been pointed out.